be an acute triangle with 
,
be the projection from 
onto 
.
be a point on the extension of 
past 
.
be on the perpendicular bisector of 
such that 
are on the same side of ![\[\frac12\angle ALE=1.4\angle ABE+3.4\angle ACE-558^\circ\]](http://latex.artofproblemsolving.com/c/6/3/c63eeb053f1fa8a29bef93516814ae121382219e.png)
Let the reflection of 
be 
and 
,
and 
such that 
.
and 
intersect the circumcircles of 
and 
at 
and 
,
and 
intersect 
and 
at 
and 
.
intersect 
.
.
chessboard into 
non-overlapping rectangles subject to the following conditions:
is the number of white squares in the 
-
.
.
denote the determinant of a square matrix 
.![$g:\left[0, \frac{\pi}{2}\right] \rightarrow R$](http://latex.artofproblemsolving.com/5/3/4/534fcbbc20e62de2dfa2579cd0642663c9fc3380.png)
be the function defined by
where 
.
be a quadratic polynomial whose roots are the maximum and minimum values of the function 
and 
.
Y by Adventure10, Mango247
Let 
be a rhombus of sides 
. On the side 
construct the rhombus 
outside and such that the side 
is parallel to the diagonal 
of . If the area of is equal to 
, calculate the area of .
be a rhombus of sides 
. On the side 
construct the rhombus 
outside and such that the side 
is parallel to the diagonal 
of . If the area of is equal to 
, calculate the area of .This post has been edited 1 time. Last edited by parmenides51, Jun 7, 2024, 6:40 PM
be a point in 
such that 
.
be the intersection of the diagonals of 
is 
.
.
,
.
.
.
